You need to run a better test than a single check on the alternator. You don't mention mileage, but things do wear out. That generation also had buggy VRs, which is piggybacked onto the alternator and, as it happily turns out, also contain the brushes. My guess is that you're getting intermittent charging, either from a flaky VR or worn brushes.

That said, this is how I would proceed.

Cold engine, remove the serpentine belt and spin the alternator pulley, testing for noise, smoothness and excess play. If it checks out then test the other pulleys with a bit of extra attention to the tensioner (it could be letting the belt slip under some conditions) and the idler pulley. (Side note: if you still have the old-style tensioner where you can see the nut on the threaded shaft securing the pulley, I would change it, MB redesigned it someplace around 03-04 and for good reason, the older design can fail catastrophically and cause significant collateral damage.)

If that checks out, then I'd inspect the connections to the alternator as well as the ground strap on the engine, in fact I'd pull the ground strap so I could clean the connections. Depending on where you live that can all wear out and oxidize. Usually this shows up first as occasional starting issues, but it's free to inspect, clean and refit, other than your time.

And how is your battery? Dealers will happily give you a free multipoint inspection (some even include a free car wash) hoping to find things that will fill their coffers. One of those is a comprehensive battery test; if you have a flaky cell it will show up and that can trigger the alert as system voltage fluctuates.

But if the alternator is nice and quiet, the grounds are good and the battery is good, then I would change the VR.

Good luck.